There is little doubt that Donald Trump was more enthused about the day he spent at Windsor Castle than his talks with Sir Keir Starmer at Chequers.

And that is no slight on the UK prime minister's hospitality during this state visit, which Trump and his team have been eager to praise.

Starmer's country residence is undoubtedly an impressive meeting place, and there was even an aerial display by the British Army's Red Devils who flew enormous British and American flags to welcome the US leader to the Buckinghamshire countryside.

But as much as Trump appears to genuinely like Starmer, with their warm relationship on display at a joint news conference on Thursday, the president was totally beguiled by being hosted by the King and Queen on Wednesday.

According to his chief of staff, Susie Wiles, his definitive highlight of the trip was the elaborate evening banquet for 160 guests in Windsor Castle's St George's Hall that evening.

For Trump, who has a deep and longstanding admiration for the Royals, it is hard to compete with being toasted by the King. No matter how many jets are laid on for you in the skies above Chequers.

State visits like these allow presidents and prime ministers to connect with one another on a more personal level, and offer a chance for their respective staff to build working relationships. They are also an opportunity to demonstrate the closeness of relations on a big stage.

In this sense, it was smooth sailing for both sides.

However, there are limits to how much influence any leader can have on Trump, regardless of the success of a trip such as this. Inside Chequers, I asked Wiles how much difference it will make to Britain's ability to influence US policy on trade, tariffs and international affairs. Her response was frank – none at all.

However much Trump enjoyed this state visit, he is not going to alter his positions on important global matters because of a memorable night spent at Windsor Castle.

But after all the pomp and pageantry, Starmer appears to have at least earned the right to respectfully disagree with Trump without paying a diplomatic penalty. It can be costly to get on the wrong side of the US president, but by carefully navigating the relationship the UK has managed to avoid the punishingly high trade tariffs that have been imposed on other nations.

Starmer, meanwhile, has not been subjected to a humiliating dressing down or given a derogatory nickname.

While this was never going to descend into the kind of awkward clash we've seen at times in the Oval Office this year, it is notable that Trump approached the questions during the concluding news conference in a far less combative way than he often does back in Washington.

Did the UK prime minister play his trump card by arranging this lavish state visit? It was choreographed flawlessly and clearly delighted Trump and the first lady.

Although Starmer may not have won the ability to change the president's mind, he can disagree with him without jeopardising relations. For that reason, a falling out now feels further away than ever before.